Question

please help

Answer 1

First of all, you know the Argand Diagram is drawn like so. Let's do the first part first. The point \(1 + i\sqrt{3}\) has x = 1, y = \(\sqrt{3}\), right?

Answer 2

yes

Answer 3

To figure out what \(|z - 1 - i\sqrt3| \le 1\) is, let \(z = x + yi\). Substituting in, \(|z - 1 - i\sqrt3| \le 1 \implies |(x - 1) + (y - \sqrt{3})i| \le 1\). Do you think you can simplify this inequality into a form that you are familiar with?

Answer 4

its a circle with centre \[1+i \sqrt{3}\] ??

Answer 5

Yes! So, putting it onto our graph now,